## Step 1: Define the symbolic representation of the variables
The variables are: ['chrysanthemums', 'daisies', 'aloe vera', 'hydrangeas', 'cherry trees']. 
Let's denote them as $x_1, x_2, x_3, x_4, x_5$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is: 
$1 \cdot x_1^2 + 6 \cdot x_1 \cdot x_2 + 5 \cdot x_1 \cdot x_3 + 1 \cdot x_1 \cdot x_4 + 9 \cdot x_1 \cdot x_5 + 7 \cdot x_2^2 + 4 \cdot x_2 \cdot x_3 + 6 \cdot x_2 \cdot x_4 + 1 \cdot x_2 \cdot x_5 + 6 \cdot x_3^2 + 6 \cdot x_3 \cdot x_4 + 3 \cdot x_3 \cdot x_5 + 7 \cdot x_4^2 + 3 \cdot x_4 \cdot x_5 + 1 \cdot x_5^2 + 6 \cdot x_1 + 1 \cdot x_2 + 8 \cdot x_3 + 9 \cdot x_4 + 9 \cdot x_5$.

## Step 3: List the constraints in symbolic notation
Constraints:
1. $9x_1 \leq 182$
2. $22x_1 \leq 385$
3. $7x_2 \leq 182$
4. $17x_2 \leq 385$
5. $7x_3 \leq 182$
6. $18x_3 \leq 385$
7. $22x_4 \leq 182$
8. $7x_4 \leq 385$
9. $3x_5 \leq 182$
10. $18x_5 \leq 385$
11. $x_1^2 + x_2^2 \geq 35$
12. $x_1 + x_5 \geq 32$
13. $x_2 + x_5 \geq 12$
14. $x_3 + x_4 \geq 21$
15. $x_1 + x_2 + x_4 \geq 30$
16. $x_1^2 + x_4^2 \geq 33$
17. $x_3^2 + x_4^2 \geq 25$
18. $x_1 + x_5 \geq 46$
19. $x_4 + x_5 \geq 34$
20. $x_1^2 + x_2^2 \geq 48$
21. $x_3^2 + x_5^2 \geq 32$
22. $7x_1 - 5x_5 \geq 0$
23. $x_1 + x_2 \leq 129$
24. $x_2^2 + x_4^2 \leq 128$
25. $x_1 + x_4 \leq 105$
26. $x_4 + x_5 \leq 138$
27. $x_1 + x_3 \leq 179$
28. $x_1 + x_5 \leq 104$
29. $x_3^2 + x_5^2 \leq 145$
30. $x_2^2 + x_4^2 + x_5^2 \leq 147$
31. $x_1^2 + x_3^2 + x_5^2 \leq 84$
32. $x_1 + x_2 + x_3 + x_4 + x_5 \leq 84$
33. $22x_1 + 7x_4 \leq 257$
34. $17x_2 + 18x_3 \leq 246$
35. $22x_1 + 18x_5 \leq 259$
36. $22x_1 + 17x_2 + 18x_3 + 7x_4 + 18x_5 \leq 259$

## Step 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'chrysanthemums'), 
        ('x2', 'daisies'), 
        ('x3', 'aloe vera'), 
        ('x4', 'hydrangeas'), 
        ('x5', 'cherry trees')
    ], 
    'objective_function': '1*x1^2 + 6*x1*x2 + 5*x1*x3 + 1*x1*x4 + 9*x1*x5 + 7*x2^2 + 4*x2*x3 + 6*x2*x4 + 1*x2*x5 + 6*x3^2 + 6*x3*x4 + 3*x3*x5 + 7*x4^2 + 3*x4*x5 + 1*x5^2 + 6*x1 + 1*x2 + 8*x3 + 9*x4 + 9*x5', 
    'constraints': [
        '9*x1 <= 182',
        '22*x1 <= 385',
        '7*x2 <= 182',
        '17*x2 <= 385',
        '7*x3 <= 182',
        '18*x3 <= 385',
        '22*x4 <= 182',
        '7*x4 <= 385',
        '3*x5 <= 182',
        '18*x5 <= 385',
        'x1^2 + x2^2 >= 35',
        'x1 + x5 >= 32',
        'x2 + x5 >= 12',
        'x3 + x4 >= 21',
        'x1 + x2 + x4 >= 30',
        'x1^2 + x4^2 >= 33',
        'x3^2 + x4^2 >= 25',
        'x1 + x5 >= 46',
        'x4 + x5 >= 34',
        'x1^2 + x2^2 >= 48',
        'x3^2 + x5^2 >= 32',
        '7*x1 - 5*x5 >= 0',
        'x1 + x2 <= 129',
        'x2^2 + x4^2 <= 128',
        'x1 + x4 <= 105',
        'x4 + x5 <= 138',
        'x1 + x3 <= 179',
        'x1 + x5 <= 104',
        'x3^2 + x5^2 <= 145',
        'x2^2 + x4^2 + x5^2 <= 147',
        'x1^2 + x3^2 + x5^2 <= 84',
        'x1 + x2 + x3 + x4 + x5 <= 84',
        '22*x1 + 7*x4 <= 257',
        '17*x2 + 18*x3 <= 246',
        '22*x1 + 18*x5 <= 259',
        '22*x1 + 17*x2 + 18*x3 + 7*x4 + 18*x5 <= 259'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name='chrysanthemums', vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name='daisies', vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name='aloe_vera', vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name='hydrangeas', vtype=gurobi.GRB.INTEGER)
x5 = m.addVar(name='cherry_trees', vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(1*x1**2 + 6*x1*x2 + 5*x1*x3 + 1*x1*x4 + 9*x1*x5 + 7*x2**2 + 4*x2*x3 + 6*x2*x4 + 1*x2*x5 + 6*x3**2 + 6*x3*x4 + 3*x3*x5 + 7*x4**2 + 3*x4*x5 + 1*x5**2 + 6*x1 + 1*x2 + 8*x3 + 9*x4 + 9*x5, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(9*x1 <= 182)
m.addConstr(22*x1 <= 385)
m.addConstr(7*x2 <= 182)
m.addConstr(17*x2 <= 385)
m.addConstr(7*x3 <= 182)
m.addConstr(18*x3 <= 385)
m.addConstr(22*x4 <= 182)
m.addConstr(7*x4 <= 385)
m.addConstr(3*x5 <= 182)
m.addConstr(18*x5 <= 385)
m.addConstr(x1**2 + x2**2 >= 35)
m.addConstr(x1 + x5 >= 32)
m.addConstr(x2 + x5 >= 12)
m.addConstr(x3 + x4 >= 21)
m.addConstr(x1 + x2 + x4 >= 30)
m.addConstr(x1**2 + x4**2 >= 33)
m.addConstr(x3**2 + x4**2 >= 25)
m.addConstr(x1 + x5 >= 46)
m.addConstr(x4 + x5 >= 34)
m.addConstr(x1**2 + x2**2 >= 48)
m.addConstr(x3**2 + x5**2 >= 32)
m.addConstr(7*x1 - 5*x5 >= 0)
m.addConstr(x1 + x2 <= 129)
m.addConstr(x2**2 + x4**2 <= 128)
m.addConstr(x1 + x4 <= 105)
m.addConstr(x4 + x5 <= 138)
m.addConstr(x1 + x3 <= 179)
m.addConstr(x1 + x5 <= 104)
m.addConstr(x3**2 + x5**2 <= 145)
m.addConstr(x2**2 + x4**2 + x5**2 <= 147)
m.addConstr(x1**2 + x3**2 + x5**2 <= 84)
m.addConstr(x1 + x2 + x3 + x4 + x5 <= 84)
m.addConstr(22*x1 + 7*x4 <= 257)
m.addConstr(17*x2 + 18*x3 <= 246)
m.addConstr(22*x1 + 18*x5 <= 259)
m.addConstr(22*x1 + 17*x2 + 18*x3 + 7*x4 + 18*x5 <= 259)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('chrysanthemums: ', x1.varValue)
    print('daisies: ', x2.varValue)
    print('aloe_vera: ', x3.varValue)
    print('hydrangeas: ', x4.varValue)
    print('cherry_trees: ', x5.varValue)
else:
    print('No solution found')
```